45
OPTIMAL LOAD FREQUENCY CONTROL OF TWO AREA POWER SYSTEM
P. O. Oluseyi*, K. M. Yellow, T. O. Akinbulire, O. M. Babatunde and A. S. Alayande
Department of Electrical/Electronics Engineering, University of Lagos, Akoka, Lagos, Nigeria
*Corresponding Author’s Email: [email protected]
ABSTRACT
Modern power systems are operated under various constraints which are meant to ensure an appropriate delivery of service.
Meanwhile power system faces imbalance in power generation and its consumption in which the higher the load consumption
the lower the frequency of operation. The governor-turbine combination will then experience a devastating reduction in its
frequency of operation due to disturbance that may lead to system collapse. Both governor and turbine are included in the
model of this power system. The control objective is to regulate the frequency error, tie-line power error and area control error
despite the presences of external load disturbance (0.01 pu) and system uncertainties. Various control policies were investigated
using various combinations of system parameters on a platform of a series of combination of the PI, fuzzy logic and neuro-fuzzy
controller with the power system for better stability. This could be found in the other approaches. The neuro-fuzzy based
controller load frequency controller is simulated on this two-area interconnected nonlinear power system. To verify the
performance of the various controllers, the data from a typical hydrothermal power grid was adapted for the study. From the
simulation results; it was recorded the neuro-fuzzy controller enjoyed a settling time of 5 seconds while under the same
operating condition the system stability is achieved at 12 seconds using the PI controller. This, thus, demonstrates the
robustness of the neuro-fuzzy controller in contrast to the fuzzy logic and proportional-integral (PI) controllers. This thus shows
that the neuro-fuzzy logic controller is superior to the other two considered in this work. Hence for a two-area network, the
neuro fuzzy approach is recommended for the steady state operation of the system so as to ensure the dynamic stability of the
network.
Keywords: Power system, load frequency, neuro-fuzzy, controller, hydro-thermal, proportional-integral.
INTRODUCTION
In a modern power system, several sources of electric energy
are integrated to meet the increasing national energy demand.
In doing this, diverse energy sources are combined to supply
the load centres. These may include gas, hydro, thermal,
nuclear, photovoltaic, etc. Due to these distinct sources
supplying a transmission network that needs to operate at a
nominal frequency of 50 Hz; then it is crucial to optimally
maintain reliability and quality of supply by instituting the
principle of control strategy. The ability to optimally match
the load demand to power generated as well as a fast system
response to frequency variation helps to improve power
system performance. Stable operation of power system
requires matching the total generation with total load demand
at little or no system losses. Due to the dynamism in load
demand with respect to time, the real and reactive power
balance is disturbed. This results in deviation of system
frequency and tie-line interchange power from their
scheduled value. High deviation of system frequency can lead
to system collapse. This has necessitated the design of load
frequency controller (LFC) for system states (such as area
frequency, and tie-line interchange power) regulation. LFC is
one of the most important ancillary services required for a
smooth and secure operation of power system (Qian et al.,
2013; Prakash et al., 2015).
In any interconnected power system, the dynamic load
variation is a common phenomenon; especially in hydro-
thermal power systems. In other words, demand for energy
keeps varying; this change in demand always influences the
system frequency. If this frequency is not properly managed;
it may result impact the system reliability and quality of the
power output. If this continues unabated; it may lead to
system collapse. To achieve high design capabilities of load
frequency control, different controllers based on fuzzy logic
controller (FLC) as well as conventional controllers are
considered by researchers. The peak overshoot and settling
time of fuzzy controllers have been generally shown to be
lower than those of conventional proportional integral (PI)
controllers (Zamee et al., 2013; Ammisetty et al., 2016).
Fuzzy logic controllers also give better dynamic performance
and reduce the oscillation of frequency of deviation when
compared to conventional PI controller (Chaturvedi and
Dwivedi, 2014). Conventional controllers are very simple to
implement and sometimes give acceptable dynamic response.
However, they are limited by slow response, lack of
efficiency and poor handling of system nonlinearities when
system complexity in real-time solution occurs due to
increasing load variation without equitable change in
generation which may influence further system disturbance.
This study aim is to optimize the control of load frequency in
a hydro thermal power system. In order to achieve this aim,
this study considered modelling of speed governor, turbine,
generator, and load of a hydro plants and thermal plant,
developing a mathematical model of load frequency control
of the hydro thermal power system, and developing an
optimal load frequency control technique suitable for the
hydro-thermal system.
The frequency of power transmission system is determined
by the active power which in turn is determined by the
system’s power generation/load mismatch. Therefore, in
order to control the frequency of the system, it is imperative
that there is need to take into account the speed of the electric
governor system (primary control) as well as provide a speed
droop control mechanism (secondary control) for the system.
This ensures that while the load increases tasking the
Nigerian Journal of Engineering Faculty of Engineering Ahmadu Bello University Samaru-Zaria, Nigeria
Vol. 26, No. 2, August 2019 ISSN: 0794 - 4756
46
generator for more power output; the droop system reduces
the governor reference speed. Hence, the control systems
consist of two control levels. The primary control which
relates to the governor and turbine dynamics is a mechanical
system with a relatively slow response time. On the other
hand, the secondary control relates to the droop control
mechanism and has a relatively faster dynamics. In addition
to these control loops, the power system typically consists of
supplementary and auxiliary controls such as the power
system stabilizer. In order to design a control system, it is
imperative to get the power system model with adequate
complexity. Most of the works reported in the literature have
been carried out by considering various linearized model of
thermal/ hydro of single area or multi-area power systems.
Integral of the control error are taken as control signals for
conventional control strategies of the LFC problem. In order
to obtain a desired gain and phase margins in the classical
control techniques, Bode and Nyquist diagrams, as well as
root locus, are usually often deployed. This reveals that
closed loop transient response will result to poor dynamic
performance, especially in the advent of instability
necessitated by increasing load demand which further
complicated by its negative influence on the reactive power
variation in the system. This results in parameter variations
and nonlinearities (such as the noticeable relatively large
overshoots and transient frequency deviation), even when the
design is straight forward, easy and controllable for practical
implementation (Elgerd et al., 1970; Das et al., 1990).
Quazza (1966) proposed the approach with non-interaction
between frequency and tie-line power control and each
control area responsible for its own load variations. The
technique based on coordinated system-wide correction of
time error and inadvertent interchange is incorporated for
AGC study by Cohn, 1971; Choi, et al., 1981). The
suboptimal LFC regulator designs, to deal with the practical
limitations in the implementation of LFC based on feedback
of all state variables. The design method employs model and
singular perturbation techniques to ensure the decoupling of
the interconnection of power system into its subsystem
components (Choi, et al., 1981). In the beginning, the LFC
problem was based on centralized control strategy, however,
the implementation of global controller requires information
about all the states of the power system.
Elgerd et al. (1970) suggested a feedback and loop gain to
eliminate the disturbance, and new feedback control law is
developed by using a state variable model and the state
regulator problem of optimal control theory. Decentralized
control system divides composite system to subsystems each
with a separate control, to overcome the problems arising
from centralized control. It also reduces the computational
and communication burden between different systems and
makes the control more feasible and simple. Yang et al.
(1998) proposed decentralized LFC based on structured
singular values. Shayeghi et al. (2008) technique is presented
in 3-area interconnected power system. Two-level or multi-
level control scheme is used to overcome instability in power
system due to strong interactions between control areas
(Babahajiani et al., 2016; Parvaneh et al., 2016;
Satheeshkumar and Shivakumar, 2016). Premakumaran et al.
(1982) proposed some aspects of multilevel LFC of a two-
area power system. Their study incorporates the effects of
governor controls and an excitation system.
A global controller, capable of exploiting the possible
beneficial aspects of interconnections, has been applied in the
LFC study (Ray and Rani 2001) whereby favourable results
were reported. Pande and Kansal (2015) investigated the
influence of the integral controller on the hybrid of the
conventional method of LFC with the artificial intelligence
(AI) technique based fuzzy logic controller to solve with the
power system collapse or system instability problem for
multi-area system. This work was reported to have
considerably reduced the unscheduled tie-line power flow
between neighbouring control areas. Furthermore, these
controllers provided a robust system which was more stable
and reliable and helped the system to regain its nominal
operating condition with zero steady state error after any
disturbance. The system stabilized with less settling time but
there was a little deviation from the nominal frequency value
at the application of integral controller with the fuzzy
controller; thus the system stabilized with less settling time at
zero steady state error.
However, the Artificial Intelligence (AI) techniques such as
FLC and Artificial Neural Network (ANN) have been applied
for load frequency control to overcome these limitations of
the conventional methods (Aravindan et al., 2009). It was
discovered that the ANN-based approached tend to perform
better when the power system is non-linear and of high
complexity. As the power system model utilised in this study
contains such high non-linearity and complexity, an ANN-
based approach is considered in this study because its
proficient satisfactory control performance when compared
with conventional controllers in such a situation (Surya et al.,
2013). Sharma and Bhadoriya (2015) discussed the dynamic
performance of automatic load frequency control of a three-
area power system using Proportional-Integral-Derivative
(PID) controller to reduce settling time and oscillations as
well as to improve the response time. Shayeghi et al. (2006),
developed a multi-stage controller that utilized the fuzzy
switch to blend a proportional derivative (PD) fuzzy logic
controller with an integral fuzzy logic input. This revealed its
tendency of high insensitivity to large load changes and
disturbances in the presence of plant parameter variations and
system nonlinearities. The benefit was that it didn’t require an
accurate model of the AGC problem, and the design process
is lower than that of the other fuzzy PID controllers.
Parvaneh et al. (2016) developed optimum load LFC of a
multi-area power system using PID controller parameter
regulation based on a heuristic optimization technique called
seeker optimization algorithm to eliminate the power system
oscillations. The result of controller of provides better
damping in comparison genetic algorithm and particle swarm
optimisation based PID controllers. Zamee et al. (2013)
proposed the use of conventional PI controller and artificial
intelligence to study the load frequency control of
interconnected power system. In the proposed scheme, a
control methodology is developed using conventional PI
controller and FLC for interconnected hydro-thermal power
system. The control strategies guarantee that the steady state
error of frequencies and inadvertent interchange of tie-lines
power are maintained in a given tolerance limitations. Thus,
FLC performed better than conventional PI controller when
some disturbance in load is given to the system.
Nigerian Journal of Engineering Vol. 26, No. 2, August 2019
47
Altas and Neyens (2006) designed a simulation model of a
fuzzy logic based load frequency controller model for power
systems and it was compared with the classical regulating
systems in order to verify and show the advantages of the
model and controller developed. The results obtained showed
that the output of the load change was controlled with less
overshoot and shorter settling time. Qian et al. (2013)
proposed a neural sliding-mode load method for LFC of
power systems with the governor dead band (GDB)
nonlinearity; an additional state is introduced to the control
system. A sliding-mode controller is designed for the linear
nominal system with no GDB, and a neural compensator is
proposed to compensate GDB. In this case, the controller and
compensator work together to realize robust control of the
nonlinear system. The weight update formula of the network
is deduced from Lyapunov direct method. It is proven that the
controller and compensator are able to ensure that the control
system is of asymptotic stability. Simulation results illustrate
the validity and robustness of the proposed method via a
single-area power system with governor dead band (GDB).
Pande and Kansal (2015) and Prakash et al. (2015) discussed
two-area-hydro-thermal power system connected through tie-
lines, the perturbation of frequencies at the areas and
resulting tie-line power flows arise due to unpredictable load
variations that cause mismatch between the power generated
and demanded. The performance of the intelligent adaptive
neuro-fuzzy interface system (ANFIS) controllers was
compared with ANN, fuzzy and conventional PI, PID based
approaches and thus showed better dynamic response. Shree
and Kamaraj (2016) proposed a hybrid neuro-fuzzy for
automatic generation control in restructured power system; its
control strategy is insensitive to load variations and
disturbances in the advent of system nonlinearities and
variance in the plant parameters. This was deployed on a
three-area-hydropower generation system.
From foregoing, there are some areas of research that was not
covered by the past research. Among which are the control
strategy of the hybrid hydrothermal generation systems. The
classical control and heuristic control methods have been
severally explored as control strategies for the power system
stability and control. This latest research shall investigate the
neuro-fuzzy controller for the assessment of hydrothermal
power system.
MATERIALS AND METHIOD
Materials
Some of the tools for executing this research are the PI
controllers which is employed for generating the
conventional results, so also was the fuzzy logic controllers
which was for training the data collected for the sake of the
analysis; the data of the two-area hydrothermal power system
with tie line. A single area power system is as shown in
Figure 1 while the tie line is as depicted in Figure 2.
Figure 1: Block diagram representation of single area
Figure 2: Block diagram representation of a tie line
∑
−
+ +
∑
−
Controller
+ ∑
P. O. Oluseyi, K. M. Yellow, T. O. Akinbulire, O. M. Babatunde and A. S. Alayande
Optimal Load Frequency Control of Two Area Power System
48
Method
This involves the deployment of mathematical model and
simulation of same to achieve the desired goal. This is done
using the control strategy.
Mathematical Model
The tie line model is developed from first principle by
considering power from Area 1 to 2 (Equation 1). When the
direction of power transfer is change from Areas 2 to 1,
Equation (1) becomes Equation (2).
(1)
(2)
where, and represents are power angles of end
voltages and of equivalent machine in the two area,
respectively, represents the reactance of the tie line
which also shows positive direction in the flow of tie line
power, represents small deviations in and
, respectively.
The relational change in power can be expressed as Equation
(3). This therefore formed the basis of further analysis of the
tie line model (Equation 4).
to (3)
(4)
] (5)
Since for small values and
, Equation (5) is
expressed as Equation (6).
(6)
By considering Equation (2), this study modified Equation (6)
as Equation (7). This is also modified by considering Torque
product (Equation 8). This equation is defined as the
synchronizing co-efficient of a line owing to the t electric
stiffness of synchronous machines.
(7)
(8)
where, Torque product.
The change in frequency is considered in order to eliminate
the small deviations in and in Equation (8). The
relationship between frequency and change in power angles is
expressed as Equation (9).
(9)
(10)
(11)
By considering Equation (9), Equation (8) is modified as
Equation (12). Laplace transform is used to convert Equation
(12) to Equation (13). However, when power transfer is from
Area 2 to 1, Equation (13) becomes Equation (14).
(12)
(13)
(14)
From the Figure 1, the power balance equation is written as
the incremental power balance equation for a single area
(Equation 15). This equation changes to Equation (15) when
two areas are being considered.
(15)
(16)
Based Figure 2 and Equation (16), the expression for normal
operation of power on the tie line is given as Equation (17).
(17)
Given that and ,
Equation (17) becomes Equation (18). By substituting
Equation (17), Equation (18) was obtained as the expression
for change in frequency of a power system.
(18)
(19)
Given Equation (19), this study modified Equation (18) as
Equation (20).
(20)
Thus,
(21)
To eliminate steady state error in frequency in tie line power
flow, tie-line bias control is used. This takes care of the net
interchange and also the ration the frequency control, of the
area. Given that the area control error for Areas 1 and 2 are
and , respectively, the area control errors are
linear combination of frequency and tie line error for each
area (Equation 22 and 23).
(22)
(23)
Nigerian Journal of Engineering Vol. 26, No. 2, August 2019
49
where, and are frequency bias of Areas 1 and 2,
respectively.
By considering and as mode integral of
and , respectively (Equations 24 and 25),
Laplace transform is used to generate the expressions for
and (Equations 26 and 27).
(24)
(25)
(26)
(27)
Step changes in and are applied
simultaneously in Control Areas 1 and 2, respectively. At
steady state condition the output signals of all integrating
block will be constant and their input signal will be zero
(Equations 28 to 35).
(28)
(29)
(30)
and (31)
Constant (32)
(33)
(34)
(35)
Clearly under steady condition change in tie-line power and
frequency in either area is zero, which is shown by integration
of ACEs in the feedback loops of either area.
Simulation of a typical two area non-reheat power system
Simulink was used to design and simulate a typical two area
non-reheat power system. The model is designed and
configured appropriately to actualize design philosophy. This
led to the investigation of the operating scenario under
various combinations of parameters. In other words, the next
three diagrams (i.e. Figures 3 to 5) provided a platform for a
series of combination involving PI, fuzzy logic and neuro-
fuzzy controller as depicted by Figures 3, 4 and 5
respectively.
From Figure 3, the PI controller was pass through
perturbation with a disturbance of magnitude of 0.01 pu,
while in the case of Figure 4, a fuzzy logic controller is
experienced a disturbance of 0.01 pu; the resulting Simulink
is as shown.
Figure 3: A two area LFC using PI controller
P. O. Oluseyi, K. M. Yellow, T. O. Akinbulire, O. M. Babatunde and A. S. Alayande
Optimal Load Frequency Control of Two Area Power System
50
Fig
ure
4:
A t
wo
are
a L
FC
usi
ng
fu
zzy l
og
ic c
on
tro
ller
Nigerian Journal of Engineering Vol. 26, No. 2, August 2019
51
Fig
ure
5:
A t
wo
are
a L
FC
usi
ng
neu
ro-f
uzz
y c
on
tro
ller
P. O. Oluseyi, K. M. Yellow, T. O. Akinbulire, O. M. Babatunde and A. S. Alayande
Optimal Load Frequency Control of Two Area Power System
52
So also, from Figure 5; the neuro-fuzzy controller is used
with the data collected; this is thus trained by ANFIS. Clearly
under steady condition change in tie-line power and
frequency in either area is zero, which is shown by
integration of ACEs in the feedback loops of either area.
Thus critical review of the results of these investigations is as
presented in Section 4.
RESULTS AND DISCUSSION
In this study, the simulation results were generated for the
power system control, and then the PI controllers are used to
get conventional results. In case of the fuzzy logic
controllers, for better performance, the training data were
collected from the fuzzy logic control and used for analysis.
After that the neuro-fuzzy controller is designed for LFC of
power system and its results are compared with conventional
PI, fuzzy logic load frequency controller for a two-area power
system.
Simulation of a Typical Two Area Non-Reheat Power
System
Simulink was deployed to design and simulate a typical two
area non-reheat power system. The model is designed and
configured appropriately to actualize the system design
philosophy. Thus this section presents the results of the
various analysis under different scenarios for te examination
of network behaviour to the variation in system parameter
under the advent of disturbance. This is done using the
philosophy of the load frequency control of interconnected
two area power system using PI, fuzzy logic and neuro-fuzzy
controller, respectively. The effectiveness of neuro-fuzzy
controller which was tuned with bi-section method is
validated through the simulation results. The responses
shown below are the dynamic responses of each area
frequency as well as the nature of the power flow of tie line,
for the two-area power system model. In this study, first an
optimal control law is generated for the power system
control, and then the PI controllers are used to get
conventional results. In case of the fuzzy logic controllers, for
better performance, the training data were collected from the
fuzzy logic control and used for analysis. After that the
neuro-fuzzy controller is designed for LFC of power system
and its results are compared with conventional PI, fuzzy logic
load frequency controller for a two-area power system.
Change in Frequency
The results for change in frequency from the PI, fuzzy logic
and neuro-fuzzy controllers were different as there are
variations in the levels at which they attain stability in change
in frequency (see Figures 6 to 8). The neuro-fuzzy controller
was able to achieve early stability (5 sec) in change in
frequency when its performance was compared with that of
the PI and fuzzy logic controllers (see Figure 8). The level of
fluctuation in frequency of the PI controller is greater than
that of the fuzzy logic and neuro-fuzzy controllers (see
Figures 7 and 8). It took the PI controller about 12 seconds
before it was able to attain stability. The change in frequency
from the PI controller exhibited the same pattern as the fuzzy
logic controllers (Figures 6 and 7).
From Figure 5 neuro-fuzzy controller is used with the data
collected and trained by ANFIS.
Figure 6: Change in frequency using a PI controller
Nigerian Journal of Engineering Vol. 26, No. 2, August 2019
53
Figure 7: Change in frequency using a fuzzy logic controller
Figure 8: Change in frequency using a neuro-fuzzy controller
P. O. Oluseyi, K. M. Yellow, T. O. Akinbulire, O. M. Babatunde and A. S. Alayande
Optimal Load Frequency Control of Two Area Power System
54
However, the fuzzy logic controller was able to return to a
zero change in frequency, while the PI controller returned to
a stable change in frequency of about - 2.4 Hz. The fuzzy
logic controller exhibited a smooth rise in change in
frequency before it attains a stability state. This feature was
not exhibited by the neuro-fuzzy controller. The characteristic
of the neuro-fuzzy controller before it attained a stability state
was a rise and fall pattern (Figure 8).
Change in Power
Figures 9 to 11 showed that the analysis of change in power
of a hydro-thermal plant is dependent on the type of
controller that is considered. None of the three controllers
exhibited the same trend in terms of change in power.
However, the PI and fuzzy logic controls showed that they
had an initial increase in change in power, while the neuro-
fuzzy controller exhibited an initial decrease in change in
power. The level of change in power from the PI controller is
less than that of the fuzzy logic and neuro-fuzzy controllers
(see Figure 10 and 11). However, the average change in
power from the fuzzy controller is more than that of the
neuro-fuzzy controller, while they both attained stability at
almost the same time (5 sec). In addition, the fuzzy control
had more number of fluctuations before attaining stability
than the neuro-fuzzy controller.
Figure 9: Change in power using a PI controller
Figure 10: Change in power using a fuzzy logic controller
Nigerian Journal of Engineering Vol. 26, No. 2, August 2019
55
Figure 11: Change in power using a neuro-fuzzy controller
POWER DEVIATION IN TIE LINE
The power deviation graphs of the PI, fuzzy logic and neuro-
fuzzy controllers (Figures 12 to 14) did not exhibit the same
attributes. The PI controller results for power deviation
showed that it took more time to reach a stable power
deviation when compared with the fuzzy logic (Figure 13)
and neuro-fuzzy controllers (Figure 14). The PI controller
showed its lacks the ability to return back to a zero power
deviation, while fuzzy logic and neuro-fuzzy controllers were
able to return about to zero power deviations. The
performance of the neuro-fuzzy controller showed that it has
the capacity to stabilise power deviation of the hydro-thermal
plant within a short period. However, it exhibited an
abnormal feature at an early stage of trying to achieve
stability in power deviation (Figure 14). This characteristic of
the neuro-fuzzy controller is different from that of the fuzzy
logic controller which showed an abnormal decrease in power
deviation that was followed by an abnormal increase in
power deviation (Figure 13). In addition, the fuzzy logic
control exhibited more instability in power deviation before
attaining its stability when compared with the neuro-fuzzy
controller.
Figure 12: Power deviation in tie line using a PI controller
P. O. Oluseyi, K. M. Yellow, T. O. Akinbulire, O. M. Babatunde and A. S. Alayande
Optimal Load Frequency Control of Two Area Power System
56
Figure 13: Power deviation in tie line using a fuzzy logic controller
Figure 14: Power deviation in tie line using a neuro-fuzzy controller
Nigerian Journal of Engineering Vol. 26, No. 2, August 2019
Time offset: 0
57
Table 1: Comparative study of the transient response of different controllers
CONCLUSIONS
From the simulation results, it was observed that the
chattering behaviour of neuro-fuzzy controller was in the
time responses of tie-line power errors (especially at the
beginning of simulation). The two reasons which can lead to
chattering relate to the systems in canonical space; fast
dynamics which were neglected in the ideal model and
utilisation of digital controllers with finite sampling rate. The
neuro-fuzzy controller uses training data from PI or fuzzy
logic, in this study data was gotten from fuzzy logic model.
Also, it was observed that deviations in frequency, power and
tie line power for LFC can be controlled and returned to the
preset valves. For a load disturbance of a two-area
interconnected power system the deviation is not shared
equally. The simulation results verified the robustness of the
controller method LFC. The simulation results also show the
superiority of the neuro-fuzzy controller in LFC to PI and
fuzzy logic controllers in terms of settling time and overshoot
percentage.
REFERENCES
Ammisetty J., Kumar S. R. S. and Prasanth, B. V. (2016).
Load frequency control, of interconnected hydro-thermal
power system using fuzzy and PI controller. International
Journal and Magazine of Engineering, Technology,
Management and Research, 3, 160-165.
Altas, İ. H. and Neyens, J. (2006). A fuzzy logic load-
frequency controller for power systems. In International
symposium on mathematical methods in engineering,
MME06, cankayauniversity, Ankara, turkey April (pp. 27-
29).
Aravindan, P. and Sanavullah, M. Y. (2009). Fuzzy logic
based automatic load frequency control of two area power
system with GRC. International Journal of Computational
Intelligence Research, 5(1), 37-44.
Achievements in Electrical and Computer Engineering
(CBCONF), Tehran, Iran, May.
Babahajiani, P., Bevrani, H. and Shafiee, Q. (2016).
Intelligent Coordination of Demand Response and Secondary
Frequency Control in Multi-area Power Systems. In 1st IEEE
Conference on New Research.
Basri, F. (1999). Adaptive fuzzy gain scheduling for load
frequency control. IEEE Transactions on power systems,
14(1), 145-150.
Chaturvedi, R. and Dwivedi, B. (2014). Fuzzy and PI
controller based load frequency control of thermal-hydro
power system. International Journal of Innovative Science,
Engineering and Technology, 1(3).
Choi, S. S., Sim, H. K. and Tan, K. S. (1981). Load
frequency control via constant limited-state feedback.
Electric power systems research, 4(4), 265-269.
Cohn, N. (1971). Techniques for improving the control of
bulk power transfers on interconnected systems. IEEE
Transactions on Power Apparatus and Systems, (6), 2409-
2419.
Das, D., Nanda, J., Kothari, M. L. and Kothari, D. P. (1990).
Automatic generation control of a hydrothermal system with
new area control error considering generation rate constraint.
Electric Machines and Power Systems, 18(6), 461-471.
Elgerd, O. I. and Fosha, C. E. (1970). Optimum megawatt-
frequency control of multiarea electric energy systems. IEEE
Transactions on Power Apparatus and Systems, (4), 556-563.
Parvaneh, H., Dizgah, S. M., Sedighizadeh, M. and Ardeshir,
S.T. (2016, January). Load frequency control of a multi-area
power system by optimum designing of frequency-based PID
controller using seeker optimization algorithm. In Thermal
Power Plants (CTPP), 2016 6th Conference on (pp. 52-57).
IEEE.
Prakash, S. and Sinha, S. K. (2015). Neuro-fuzzy
computational technique to control load frequency in hydro-
thermal interconnected power system. Journal of the
Institution of Engineers (India): Series B, 96(3), 273-282.
Premakumaran, N., Parthasarathy, K., Khincha, H. P. and
Chidambara, M. R. (1982, November). Some aspects of
multilevel load-frequency control of a power system. In IEE
∆F ∆P ∆Tie
Settling
time
(sec)
Over
shoot
Under
shoot
Settling
time
(sec)
Over
shoot
Under
shoot
Settling
time
(sec)
Over
shoot
Under
shoot
Neuro-
fuzzy
A1 5.4 0.0032 0.0001 6.0 0.00104 0.0 7.0 0.000032 0.00016
A2 4.5 0.0031 0.0002 5.0 0.00110 0.0
Fuzzy
logic
A1 8.4 0.0 0.0013 6.8 0.00165 0.1 7.5 0.000020 0.00006
A2 8.2 0.0 0.0012 6.9 0.00154 0.2
PI A1 9.8 0.0 0.0033 14.4 0.00128 0.0 18.0 0.0 0.00034
A2 9.7 0.0 0.0034 13.8 0.00132 0.0
P. O. Oluseyi, K. M. Yellow, T. O. Akinbulire, O. M. Babatunde and A. S. Alayande
Optimal Load Frequency Control of Two Area Power System
58
Proceedings C (Generation, Transmission and Distribution)
(Vol. 129, No. 6, pp. 290-294). IET Digital Library.
Qian, D., Zhao, D., Yi, J. and Liu, X. (2013). Neural sliding-
mode load frequency controller design of power systems.
Neural Computing and Applications, 22(2), 279-286.
Quazza, G. (1966). Non-interacting controls of
interconnected electric power systems. IEEE Transactions on
Power Apparatus and Systems, (7), 727-741.
Ray, G. and Rani, C. S. (2001). Stabilizing decentralized
robust controllers of interconnected uncertain power systems
based on the Hessenberg form: Simulated results.
International Journal of Systems Science, 32(3), 387-399.
Sahu P. K. and Singh A. (2014). Load Frequency Control
with Adaptive Fuzzy Logic Approach for Multi Area Power
System. International Journal of Science and Research,
Samuel, I. A., Katende, J., Daramola, S. A. and Awelewa,
A.A. (2014). Review of System Collapse Incidences on the
330-kV Nigerian National Grid. International Journal of
Engineering Science Invention, 3, 55-59.
Satheeshkumar, R. and Shivakumar, R. (2016). Ant lion
optimization approach for load frequency control of multi-
area interconnected power systems. Circuits and Systems,
7(09), 2357.
Sharma S. and Bhadoriya J. (2015). Automatic Load
Frequency Control in Three Area Power System using PID
Controller. International Journal of Innovative Research in
Electrical, Electronics, Instrumentation and Control
Engineering, 3(8), 138-143.
Shayeghi, H. (2008). A robust decentralized power system
load frequency control. Journal of Electrical Engineering,
59(6), 281-293.
Shayeghi, H., Shayanfar, H. A. and Jalili, A. (2006). Multi-
stage fuzzy PID power system automatic generation
controller in deregulated environments. Energy Conversion
and management, 47(18-19), 2829-2845.
Shayeghi, H., Jalili, A. and Shayanfar, H. A. (2008). Multi-
stage fuzzy load frequency control using PSO. Energy
Conversion and Management, 49(10), 2570-2580.
Shree, S. B. and Kamaraj, N. (2016). Hybrid Neuro Fuzzy
approach for automatic generation control in restructured
power system. International Journal of Electrical Power and
Energy Systems, 74, 274-285.
Subha, S. (2014). Load frequency control with fuzzy logic
controller considering governor dead band and generation
rate constraint non-linearities. World Applied Sciences
Journal, 29(8), 1059-1066.
Talaq J. and Al-Basri F. (1999). Adaptive Fuzzy Gain
Scheduling for Load-Frequency Control. IEEE Trans Power
System, 14(1), 145-50.
Pande, S. and Kansal, R. (2015). Load Frequency Control of
Multi Area System using Integral-Fuzzy Controller.
International Journal of Engineering Research and
Applications, 5(6), 59-64.
Wang, Y., Zhou, R. and Wen, C. (1994). New robust adaptive
load-frequency control with system parametric uncertainties.
IEE Proceedings-Generation, Transmission and Distribution,
141(3), 184-190.
Yang, T. C., Cimen, H. and Zhu, Q. M. (1998). Decentralised
load-frequency controller design based on structured singular
values. IEE Proceedings-Generation, Transmission and
Distribution, 145 (1), 7-14.
Zamee, M. A., Mitra, D. and Tahhan, S. Y. (2013). Load
frequency control of interconnected hydro-thermal power
system using conventional PI and fuzzy logic controller. Int J
Energy Power Eng, 2(5), 191-196.
Nigerian Journal of Engineering Vol. 26, No. 2, August 2019